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Keywords:
finite von Neumann algebra; algebra of affiliated operators; semisimple ring; global dimension
finite von Neumann algebra; algebra of affiliated operators; semisimple ring; global dimension
Summary:
We prove that a finite von Neumann algebra ${\mathcal{A}}$ is semisimple if the algebra of affiliated operators ${\mathcal{U}}$ of ${\mathcal{A}}$ is semisimple. When ${\mathcal{A}}$ is not semisimple, we give the upper and lower bounds for the global dimensions of ${\mathcal{A}}$ and ${\mathcal{U}}.$ This last result requires the use of the Continuum Hypothesis.
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